1. Field of the Invention
The present invention relates to Ultra-Wideband Radio (UWB), and particularly to a method for compressive sensing, reconstruction, and estimation of ultra-wideband channels utilizing antenna angle dictionaries for increasing sparsity of UWB signals to facilitate reconstruction and estimation of ultra-wideband channels.
2. Description of the Related Art
There are two prominent types of UWB signals: “Impulse Radio Ultra-Wideband” (IR-UWB) and “Multicarrier Ultra wideband” (MC-UWB). The former is based on sending very short duration pulses, in order of nanoseconds, to convey information. The latter uses multiple simultaneous carriers to carry information. Each type has its relative technical pros and cons and spectrum occupancy requirements. IR-UWB is discussed herein.
IR-UWB, with its huge advantages, has been recognized as a great solution for future wireless personal networks. IR-UWB technique has the possibility of achieving Gigabits/s data rates, hundreds of meter operation range, Pico joule energy per bit, centimeter accuracy of positioning, and low-cost implementation. It also offers great flexibility of spectrum usage and allows unlicensed usage of several gigahertz of spectrum.
Unlike classical communications, in IR-UWB, no up-and-down radio frequency conversion is required; which reduces the implementation cost, and allows low power transmitter implementation.
The basic model for an unmodulated IR-UWB pulse train can be expressed as:
                              s          ⁡                      (            t            )                          =                              ∑                          i              =                              -                ∞                                      ∞                    ⁢                                                    A                i                            ⁡                              (                t                )                                      ⁢                          p              ⁡                              (                                  t                  -                                      i                    ⁢                                                                                  ⁢                                          T                      f                                                                      )                                                                        (        1        )            where Ai(t)=±√{square root over (Ep)} is the amplitude of the pulse with energy of Ep, p(t) is the normalized pulse waveform, and Tf is the frame time that is defined as the time interval in which one pulse is transmitted.
The UWB pulse waveform can be any pulse that satisfies the spectral mask1 regulatory requirements. The common pulse shapes discussed in IR-UWB literature are the Gaussian pulse and its derivatives. The reason for this name is referred to the similarity with Gaussian function that can be represented as:
                              p          ⁡                      (            t            )                          =                              1                                          2                ⁢                                  πσ                  2                                                              ⁢                      ⅇ                                                            (                                      t                    -                    μ                                    )                                2                                            2                ⁢                                  σ                  2                                                                                        (        2        )            where σ is the standard deviation of the Gaussian pulse in seconds, and μ is the delay in time for the midpoint of the Gaussian pulse in seconds. The pulse width is denoted by τp, which is a function of the standard deviation, given as τp=2πσ. The nominal center frequency and the spectrum bandwidth depend upon the pulse width. The bandwidth is approximately equal to 116% of 1/τp.
UWB receivers face several challenges, including narrowband interference cancellation, antenna design, timing synchronization, and channel estimation, among others. The extremely high bandwidth of the received IR-UWB signal (up to 7.5 GHz) requires high-speed analog-to-digital converters. For such speed, the use of ADC (Analog-to-Digital Conversion) increases, and likewise demands an accurate timing control system.
The conventional approach of sampling, however, consumes a lot of power, gives relatively low resolution, and can be expensive. Because it requires precise timing control system, the complexity of the circuitry increases. Moreover, oversampling of the received UWB signal may be required to improve the timing synchronization and channel estimation. For example, in many prior art methods, the required sampling rate is in excess of 25 GHz for an accurate UWB channel estimation. Such huge sampling rates are not easily supported by the current ADC technology. Consequently, alternative approaches for UWB receivers are needed to attain the required sampling rates and the time resolution. Many of these challenges can be reduced or mitigated by means of compressive sensing (CS) and its features. Yet, there remains the problem of optimizing CS to achieve the best possible channel sampling/estimation rates.
Thus, a method for compressive sensing, reconstruction, and estimation of ultra-wideband channels solving the aforementioned problems is desired.